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-----------------------------------------------------------------------------
Statistic identifier: St001532
-----------------------------------------------------------------------------
Collection: Posets
-----------------------------------------------------------------------------
Description: The leading coefficient of the Poincare polynomial of the poset cone.
For a poset $P$ on $\{1,\dots,n\}$, let $\mathcal K_P = \{\vec x\in\mathbb R^n| x_i < x_j \text{ for } i < _P j\}$. Furthermore let $\mathcal L(\mathcal A)$ be the intersection lattice of the braid arrangement $A_{n-1}$ and let $\mathcal L^{int} = \{ X \in \mathcal L(\mathcal A) | X \cap \mathcal K_P \neq \emptyset \}$.
Then the Poincare polynomial of the poset cone is $Poin(t) = \sum_{X\in\mathcal L^{int}} |\mu(0, X)| t^{codim X}$.
This statistic records its leading coefficient.
-----------------------------------------------------------------------------
References: [1] Dorpalen-Barry, G., Kim, J. S., Reiner, V. Whitney Numbers for Poset Cones [[arXiv:1906.00036]]
-----------------------------------------------------------------------------
Code:
# code by Jang Soo Kim
def delete_elements(P,A):
"Return the poset obtained from P by deleting the elements in A"
elms = [x for x in P.list() if x not in A]
rels = [R for R in P.relations() if R[0] not in A and R[1] not in A]
return Poset([elms,rels], cover_relations=False)
def add_bottom(P):
"Return the poset obtained from P by adding the minimum element 0."
elms = ["zero_hat"] + P.list()
rels = [["zero_hat",x] for x in P.list()] + P.relations()
return Poset([elms,rels], cover_relations=False)
def Poin(P,t,omega=0):
"""
Input:
P: a poset or a list of numbers [a,b,c,...].
If P = [a,b,c,...], then P is set to be the cell poset of the partition [a,b,c,...].
t: a variable
omega: a labeling of P which is given by default to the first lin ext of P.
Output: The Poincare polynomial of the poset P.
The bijection from linear extensions to P-transverse permutations is used.
"""
if type(P) == list:
P = Partition(P).cell_poset().dual()
if omega == 0:
omega = P.linear_extensions()[0]
poly = 0
for L in P.linear_extensions():
poly += t^(len(P)-len(get_P_transverse_permutation(P,omega,L)))
return poly
def get_P_transverse_permutation(P,omega,L):
"""
Input:
P: a poset
omega: a labeling of P
L: a linear extension of P
Output: The P-transverse permutation corresponding to L with respect to omega.
"""
Q = add_bottom(P)
pi = []
while len(L)>0:
N = next_level(Q,P,omega,L)
pi = pi + N[-1]
[Q, P, omega, L] = N[:-1]
return pi
def next_level(Q,P,omega,L):
"""
INPUT: Q,P,omega,L
Q: poset containing P
omega: labeling
L: a linear extension of P
OUTPUT: [Q1, P1, omega, L1, pi]
Q1 = P
P1 = P - minimal blocks
omega = omega
L1 = L restricted to P1
pi = P-transverse permutation of the minimal blocks in P.
"""
L1 = L
pi = []
C = [] # the list of current level elements in P
D = [] # the list of current level elements in P that are not minimal in Q
B = []
for x in L:
if x not in P.minimal_elements(): # If x is not a minimal element in P this level is done.
break
C.append(x)
if x not in Q.minimal_elements():
D.append(x)
if omega.index(x) == min([omega.index(d) for d in D]):
if len(B)>0:
pi.append(B)
B = [x]
else:
B.append(x)
pi.append(B)
Q1 = P
P1 = delete_elements(P,C)
L1 = L[len(C):]
return [Q1, P1, omega, L1, pi]
statistic = lambda P: Poin(P, QQ["q"].gen()).leading_coefficient()
-----------------------------------------------------------------------------
Statistic values:
([],1) => 1
([],2) => 1
([(0,1)],2) => 1
([],3) => 2
([(1,2)],3) => 2
([(0,1),(0,2)],3) => 1
([(0,2),(2,1)],3) => 1
([(0,2),(1,2)],3) => 1
([],4) => 6
([(2,3)],4) => 6
([(1,2),(1,3)],4) => 3
([(0,1),(0,2),(0,3)],4) => 2
([(0,2),(0,3),(3,1)],4) => 2
([(0,1),(0,2),(1,3),(2,3)],4) => 1
([(1,2),(2,3)],4) => 3
([(0,3),(3,1),(3,2)],4) => 1
([(1,3),(2,3)],4) => 3
([(0,3),(1,3),(3,2)],4) => 1
([(0,3),(1,3),(2,3)],4) => 2
([(0,3),(1,2)],4) => 1
([(0,3),(1,2),(1,3)],4) => 1
([(0,2),(0,3),(1,2),(1,3)],4) => 1
([(0,3),(2,1),(3,2)],4) => 1
([(0,3),(1,2),(2,3)],4) => 2
([],5) => 24
([(3,4)],5) => 24
([(2,3),(2,4)],5) => 12
([(1,2),(1,3),(1,4)],5) => 8
([(0,1),(0,2),(0,3),(0,4)],5) => 6
([(0,2),(0,3),(0,4),(4,1)],5) => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2
([(1,3),(1,4),(4,2)],5) => 8
([(0,3),(0,4),(4,1),(4,2)],5) => 3
([(1,2),(1,3),(2,4),(3,4)],5) => 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
([(0,3),(0,4),(3,2),(4,1)],5) => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1
([(2,3),(3,4)],5) => 12
([(1,4),(4,2),(4,3)],5) => 4
([(0,4),(4,1),(4,2),(4,3)],5) => 2
([(2,4),(3,4)],5) => 12
([(1,4),(2,4),(4,3)],5) => 4
([(0,4),(1,4),(4,2),(4,3)],5) => 1
([(1,4),(2,4),(3,4)],5) => 8
([(0,4),(1,4),(2,4),(4,3)],5) => 2
([(0,4),(1,4),(2,4),(3,4)],5) => 6
([(0,4),(1,4),(2,3)],5) => 2
([(0,4),(1,3),(2,3),(2,4)],5) => 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2
([(0,4),(1,4),(2,3),(4,2)],5) => 1
([(0,4),(1,3),(2,3),(3,4)],5) => 3
([(0,4),(1,4),(2,3),(2,4)],5) => 2
([(0,4),(1,4),(2,3),(3,4)],5) => 6
([(1,4),(2,3)],5) => 4
([(1,4),(2,3),(2,4)],5) => 4
([(0,4),(1,2),(1,4),(2,3)],5) => 3
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1
([(1,3),(1,4),(2,3),(2,4)],5) => 4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 1
([(0,4),(1,2),(1,4),(4,3)],5) => 2
([(0,4),(1,2),(1,3)],5) => 2
([(0,4),(1,2),(1,3),(1,4)],5) => 2
([(0,2),(0,4),(3,1),(4,3)],5) => 3
([(0,4),(1,2),(1,3),(3,4)],5) => 5
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3
([(0,3),(0,4),(1,2),(1,4)],5) => 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 3
([(0,3),(1,2),(1,4),(3,4)],5) => 3
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
([(1,4),(3,2),(4,3)],5) => 4
([(0,3),(3,4),(4,1),(4,2)],5) => 1
([(1,4),(2,3),(3,4)],5) => 8
([(0,4),(1,2),(2,4),(4,3)],5) => 2
([(0,3),(1,4),(4,2)],5) => 3
([(0,4),(3,2),(4,1),(4,3)],5) => 2
([(0,4),(1,2),(2,3),(2,4)],5) => 2
([(0,4),(2,3),(3,1),(4,2)],5) => 1
([(0,3),(1,2),(2,4),(3,4)],5) => 1
([(0,4),(1,2),(2,3),(3,4)],5) => 3
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
([],6) => 120
([(4,5)],6) => 120
([(3,4),(3,5)],6) => 60
([(2,3),(2,4),(2,5)],6) => 40
([(1,2),(1,3),(1,4),(1,5)],6) => 30
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 24
([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 24
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 12
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 8
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 6
([(1,3),(1,4),(1,5),(5,2)],6) => 30
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 12
([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 15
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 10
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 3
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 4
([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 4
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 4
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
([(2,3),(2,4),(4,5)],6) => 40
([(1,4),(1,5),(5,2),(5,3)],6) => 15
([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 8
([(2,3),(2,4),(3,5),(4,5)],6) => 20
([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 5
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 1
([(1,4),(1,5),(4,3),(5,2)],6) => 5
([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 5
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 5
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 2
([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 2
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 2
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 2
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
([(3,4),(4,5)],6) => 60
([(2,3),(3,4),(3,5)],6) => 20
([(1,5),(5,2),(5,3),(5,4)],6) => 10
([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 6
([(2,3),(3,5),(5,4)],6) => 20
([(1,4),(4,5),(5,2),(5,3)],6) => 5
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 2
([(3,5),(4,5)],6) => 60
([(2,5),(3,5),(5,4)],6) => 20
([(1,5),(2,5),(5,3),(5,4)],6) => 5
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 2
([(2,5),(3,5),(4,5)],6) => 40
([(1,5),(2,5),(3,5),(5,4)],6) => 10
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 2
([(1,5),(2,5),(3,5),(4,5)],6) => 30
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 6
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 24
([(0,5),(1,5),(2,5),(3,4)],6) => 6
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 8
([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 6
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 24
([(1,5),(2,5),(3,4)],6) => 10
([(1,5),(2,4),(3,4),(3,5)],6) => 10
([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 5
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 10
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 5
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 10
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 4
([(1,5),(2,5),(3,4),(5,3)],6) => 5
([(1,5),(2,4),(3,4),(4,5)],6) => 15
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
([(0,5),(1,5),(2,3),(5,4)],6) => 5
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 2
([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 3
([(1,5),(2,5),(3,4),(3,5)],6) => 10
([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 4
([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 8
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2
([(0,5),(1,5),(2,3),(2,4)],6) => 4
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 5
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 11
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 4
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 18
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 8
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 3
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 12
([(1,5),(2,5),(3,4),(4,5)],6) => 30
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 6
([(0,5),(1,5),(2,3),(3,4)],6) => 8
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 2
([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 7
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 3
([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 6
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 12
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 4
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 2
([(0,5),(1,5),(2,4),(3,4)],6) => 6
([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 6
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 4
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 12
([(2,5),(3,4)],6) => 20
([(2,5),(3,4),(3,5)],6) => 20
([(1,5),(2,3),(2,5),(3,4)],6) => 15
([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 5
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 1
([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 1
([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 1
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 1
([(2,4),(2,5),(3,4),(3,5)],6) => 20
([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 10
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 3
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 3
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 7
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 8
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 8
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 6
([(1,5),(2,3),(2,5),(5,4)],6) => 10
([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 3
([(1,5),(2,3),(2,4)],6) => 10
([(1,5),(2,3),(2,4),(2,5)],6) => 10
([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 10
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 3
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 5
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 6
([(0,5),(1,2),(1,3),(1,4)],6) => 6
([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 12
([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 18
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 8
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 11
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 6
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 8
([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 8
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 5
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(1,3),(1,5),(4,2),(5,4)],6) => 15
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 4
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 3
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 3
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 3
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 3
([(1,5),(2,3),(2,4),(4,5)],6) => 25
([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 7
([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 10
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 15
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 3
([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 3
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 3
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 5
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 5
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 3
([(0,4),(1,3),(1,5),(5,2)],6) => 10
([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 8
([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 7
([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 3
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 3
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 5
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 4
([(1,4),(1,5),(2,3),(2,5)],6) => 10
([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 10
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 6
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 3
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 10
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 6
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 8
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 6
([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 15
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 5
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 3
([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 8
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 3
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 5
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 1
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 3
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 6
([(0,4),(0,5),(1,2),(1,3)],6) => 6
([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 6
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 10
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 6
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 8
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 8
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 5
([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 10
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 7
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 2
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 2
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 5
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 3
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 3
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 1
([(1,4),(2,3),(2,5),(4,5)],6) => 15
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 5
([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 10
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 4
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 1
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 3
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 1
([(0,5),(1,3),(1,4),(5,2)],6) => 8
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 4
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 3
([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 5
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 4
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 5
([(2,5),(3,4),(4,5)],6) => 40
([(1,5),(2,3),(3,5),(5,4)],6) => 10
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 2
([(1,3),(2,4),(4,5)],6) => 15
([(1,5),(4,3),(5,2),(5,4)],6) => 10
([(1,5),(2,3),(3,4),(3,5)],6) => 10
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 4
([(0,4),(1,5),(5,2),(5,3)],6) => 5
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 6
([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 4
([(1,5),(3,4),(4,2),(5,3)],6) => 5
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 1
([(1,4),(2,3),(3,5),(4,5)],6) => 5
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
([(0,5),(1,4),(4,2),(5,3)],6) => 1
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 3
([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 1
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 1
([(1,5),(2,3),(3,4),(4,5)],6) => 15
([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 5
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 3
([(0,5),(1,4),(2,3)],6) => 4
([(0,5),(1,3),(2,4),(2,5)],6) => 4
([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 4
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 6
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 3
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 10
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 3
([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 7
([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 4
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 5
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 10
([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 8
([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 8
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 6
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 6
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 1
([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 10
([(0,5),(1,3),(4,2),(5,4)],6) => 6
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 5
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 2
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 2
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 3
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
([(0,5),(1,3),(2,4),(4,5)],6) => 10
([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 6
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 8
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 4
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 3
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4
([],7) => 720
([(5,6)],7) => 720
([(4,5),(4,6)],7) => 360
([(3,4),(3,5),(3,6)],7) => 240
([(2,3),(2,4),(2,5),(2,6)],7) => 180
([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 144
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 120
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 120
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 60
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 40
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 30
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 24
([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => 144
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 60
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 72
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 48
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 36
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 6
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => 6
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 8
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => 10
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => 10
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7) => 10
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => 10
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 15
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => 20
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 20
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => 20
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 20
([(2,4),(2,5),(2,6),(6,3)],7) => 180
([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => 72
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 40
([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 90
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 60
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 12
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 12
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 12
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 12
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 12
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 4
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => 5
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 4
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 5
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 12
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7) => 4
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => 4
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => 4
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => 5
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 3
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => 18
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 3
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => 5
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => 3
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 24
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => 5
([(1,4),(1,5),(1,6),(5,3),(6,2)],7) => 24
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 24
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => 4
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => 4
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 4
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 5
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 7
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 10
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 5
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7) => 10
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 10
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => 10
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7) => 10
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 10
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 4
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7) => 4
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7) => 4
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7) => 4
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 4
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 4
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 4
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 5
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7) => 4
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 7
([(3,4),(3,5),(5,6)],7) => 240
([(2,5),(2,6),(6,3),(6,4)],7) => 90
([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 48
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 30
([(3,4),(3,5),(4,6),(5,6)],7) => 120
([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 30
([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => 6
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => 2
([(2,5),(2,6),(5,4),(6,3)],7) => 30
([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 30
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 30
([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => 12
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => 3
([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 1
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 1
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 1
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => 12
([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7) => 3
([(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 12
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) => 12
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7) => 6
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 6
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => 6
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 12
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) => 12
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => 6
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 3
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2
([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => 6
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => 3
([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7) => 6
([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 6
([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7) => 6
([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => 6
([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 6
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => 6
([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 6
([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 60
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => 12
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 2
([(4,5),(5,6)],7) => 360
([(3,4),(4,5),(4,6)],7) => 120
([(2,6),(6,3),(6,4),(6,5)],7) => 60
([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 36
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 24
([(3,4),(4,6),(6,5)],7) => 120
([(2,5),(5,6),(6,3),(6,4)],7) => 30
([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => 12
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 6
([(4,6),(5,6)],7) => 360
([(3,6),(4,6),(6,5)],7) => 120
([(2,6),(3,6),(6,4),(6,5)],7) => 30
([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 12
([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 6
([(3,6),(4,6),(5,6)],7) => 240
([(2,6),(3,6),(4,6),(6,5)],7) => 60
([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 12
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 4
([(2,6),(3,6),(4,6),(5,6)],7) => 180
([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 36
([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 6
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 144
([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 24
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 120
([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 24
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 6
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 30
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 120
([(1,6),(2,6),(3,6),(4,5)],7) => 36
([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 12
([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 48
([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 14
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 4
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 8
([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 36
([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 12
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 30
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 6
([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 12
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7) => 14
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 84
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 60
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 144
([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 24
([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 30
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 2
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 8
([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 6
([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 24
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 20
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 5
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 2
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 60
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 24
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 10
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 40
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24
([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 20
([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 5
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 60
([(2,6),(3,6),(4,5)],7) => 60
([(2,6),(3,5),(4,5),(4,6)],7) => 60
([(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 30
([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7) => 8
([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 12
([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 2
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => 2
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2
([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2
([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 60
([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 30
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7) => 8
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => 2
([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2
([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 12
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 60
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 24
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 6
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 6
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 4
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 14
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 30
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 30
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24
([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 24
([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 6
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 12
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 9
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 2
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => 5
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 22
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => 4
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 6
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) => 18
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7) => 14
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 34
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 18
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 30
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 30
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 34
([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 12
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 9
([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7) => 22
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 5
([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 10
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 12
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 18
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 34
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 34
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24
([(2,6),(3,6),(4,5),(6,4)],7) => 30
([(2,6),(3,5),(4,5),(5,6)],7) => 90
([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18
([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 3
([(1,6),(2,6),(3,4),(6,5)],7) => 30
([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 12
([(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 18
([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => 6
([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => 8
([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => 6
([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7) => 6
([(2,6),(3,6),(4,5),(4,6)],7) => 60
([(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 24
([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 6
([(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 48
([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 12
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 2
([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 14
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) => 2
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 20
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => 2
([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) => 8
([(1,6),(2,6),(3,4),(3,5)],7) => 24
([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 6
([(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 30
([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 6
([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => 14
([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => 3
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7) => 8
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 6
([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 24
([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 12
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 30
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 6
([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 16
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 12
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => 2
([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) => 14
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) => 8
([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 6
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 12
([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) => 52
([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => 20
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => 5
([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 76
([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 38
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => 15
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 4
([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 52
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 30
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 12
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 40
([(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 108
([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7) => 24
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 72
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 12
([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 30
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 2
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => 2
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 2
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 5
([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 3
([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => 6
([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7) => 33
([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 15
([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 24
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 13
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 11
([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => 13
([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7) => 5
([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => 5
([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7) => 13
([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 3
([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => 3
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 2
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => 5
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 4
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => 5
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 2
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 13
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => 5
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 2
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7) => 12
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => 18
([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) => 23
([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 11
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 12
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 40
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 15
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 8
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 16
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 1
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) => 12
([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 12
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 5
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 20
([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7) => 52
([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) => 19
([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 10
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => 5
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 2
([(2,6),(3,6),(4,5),(5,6)],7) => 180
([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 36
([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 6
([(1,6),(2,6),(3,4),(4,5)],7) => 48
([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 6
([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 12
([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 2
([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 2
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 3
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => 2
([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 36
([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) => 12
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7) => 18
([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) => 6
([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => 14
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 1
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => 2
([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 2
([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) => 24
([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 12
([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 32
([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 14
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 8
([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 20
([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 10
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 6
([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 24
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 4
([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 6
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 72
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 12
([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 20
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 1
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 8
([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => 9
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 3
([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) => 12
([(1,6),(2,6),(3,5),(4,5)],7) => 36
([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 36
([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7) => 18
([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7) => 6
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 18
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 6
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 12
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 36
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 14
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 14
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 12
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6
([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 14
([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 24
([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 6
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 4
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 72
([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 12
([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 18
([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7) => 9
([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 3
([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) => 12
([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 6
([(0,6),(1,6),(2,5),(3,4)],7) => 12
([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 9
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => 1
([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => 7
([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 22
([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 12
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3
([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 15
([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 12
([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => 6
([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => 18
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7) => 34
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) => 4
([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 30
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 12
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 14
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 44
([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7) => 44
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7) => 30
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24
([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 12
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 12
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 9
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 22
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => 4
([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 18
([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 12
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => 9
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 1
([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 7
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 22
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 44
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => 10
([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) => 3
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 20
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 12
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 22
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 9
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 4
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 1
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 12
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7) => 14
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 4
([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 5
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 32
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 10
([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 3
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 20
([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) => 14
([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => 4
([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) => 32
([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 44
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 6
([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 30
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 20
([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 34
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 5
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 5
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2
([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => 3
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 10
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7) => 24
([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 10
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 40
([(3,6),(4,5)],7) => 120
([(3,6),(4,5),(4,6)],7) => 120
([(2,6),(3,4),(3,6),(4,5)],7) => 90
([(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 30
([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7) => 14
([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7) => 2
([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7) => 2
([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 2
([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 6
([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 2
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7) => 2
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => 2
([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) => 2
([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 30
([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => 6
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 1
([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 6
([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7) => 6
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7) => 2
([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) => 2
([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 36
([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 18
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 3
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 4
([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 2
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 4
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) => 9
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 3
([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 3
([(3,5),(3,6),(4,5),(4,6)],7) => 120
([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 60
([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 8
([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 30
([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 6
([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 6
([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 6
([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 6
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 2
([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 24
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 16
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 8
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 6
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 24
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7) => 16
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 8
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 6
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 12
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7) => 14
([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 3
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 3
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 3
([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 42
([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 12
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 24
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 4
([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 4
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7) => 4
([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7) => 10
([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => 7
([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7) => 16
([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 8
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => 5
([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => 8
([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => 4
([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 24
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7) => 12
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 30
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 2
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 8
([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 5
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7) => 14
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => 6
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7) => 8
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 2
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 24
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7) => 6
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => 20
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 6
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 48
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => 8
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => 14
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 20
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7) => 6
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7) => 6
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7) => 14
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 20
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 4
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7) => 16
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 10
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => 8
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 4
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 12
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7) => 14
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 8
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 30
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 16
([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7) => 14
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => 5
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 30
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 24
([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 8
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => 3
([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 8
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7) => 16
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 12
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 48
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 14
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 2
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 8
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 36
([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 6
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => 20
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 1
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) => 6
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => 4
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7) => 10
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 4
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7) => 14
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => 12
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7) => 18
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 20
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 4
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 12
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 4
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2
([(2,6),(3,4),(3,6),(6,5)],7) => 60
([(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 18
([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => 8
([(2,6),(3,4),(3,5)],7) => 60
([(2,6),(3,4),(3,5),(3,6)],7) => 60
([(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 60
([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7) => 22
([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 4
([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) => 4
([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 18
([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => 4
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) => 4
([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7) => 4
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 30
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 12
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => 2
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => 2
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7) => 2
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => 9
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => 5
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => 8
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7) => 8
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 2
([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7) => 2
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 8
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 2
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 2
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7) => 2
([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 36
([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7) => 12
([(1,6),(2,3),(2,4),(2,5)],7) => 36
([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 36
([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7) => 44
([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7) => 12
([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7) => 22
([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 8
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => 14
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7) => 24
([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 24
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 24
([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 60
([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => 84
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => 40
([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 52
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => 30
([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 38
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 24
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 30
([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7) => 30
([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7) => 18
([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => 14
([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 12
([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => 72
([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 20
([(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 108
([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7) => 32
([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 48
([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 10
([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 66
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 14
([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 36
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 6
([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 48
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 8
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 8
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => 11
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 18
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 8
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7) => 14
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => 23
([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7) => 25
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 14
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Created: May 03, 2020 at 17:31 by Martin Rubey
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Last Updated: May 03, 2020 at 17:47 by Martin Rubey